Metastable states of a ferromagnet on random thin graphs

Abstract

We calculate the mean number of metastable states of an Ising ferromagnet on random thin graphs of fixed connectivity c. We find, as for mean field spin glasses that this mean increases exponentially with the number of sites, and is the same as that calculated for the +/- J spin glass on the same graphs. An annealed calculation of the number <N_{MS}(E)> of metastable states of energy E is carried out. For small c, an analytic result is obtained. The result is compared with the one obtained for spin glasses in order to discuss the role played by loops on thin graphs and hence the effect of real frustration on the distribution of metastable states.

15 pages, 3 figures

Cited by in corpus (15)

• Tapping Spin Glasses
• Zero-Temperature Relaxation of Three-Dimensional Ising Ferromagnets
• Circuits in random graphs: from local trees to global loops
• Exact Occupation Time Distribution in a Non-Markovian Sequence and Its Relation to Spin Glass Models
• Metastable states and T=0 hysteresis in the random-field Ising model on random graphs
• Steady State Behavior of Mechanically Perturbed Spin Glasses and Ferromagnets
• Inherent Structures, Configurational Entropy and Slow Glassy Dynamics
• Phase transitions in the steady state behavior of mechanically perturbed spin glasses and ferromagnets
• Hysteresis and complexity in the zero-temperature mean-field RFIM: the soft-spin version
• Metastable configurations on the Bethe lattice
• Entropy Inflection and Invisible Low-Energy States: Defensive Alliance Example
• A renewal approach to configurational entropy in one dimension
• On metastable configurations of small-world networks
• Coordination problems on networks revisited: statics and dynamics
• On the structure factor of jammed particle configurations on the one-dimensional lattice